Integral representation for the product \(I_nK_n\)  (see [1]}) :
\(\forall n\in \mathbb {N}^*,\quad \forall \lambda >0,\quad (I_{n}K_{n})(\lambda )=\frac{1}{2}\int _{0}^\infty J_0\big (2\lambda \sinh (\tfrac{t}{2})\big )e^{-nt}dt.\) 
